Compatibility of any pair of 2-outcome measurements characterizes the Choquet simplex

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Abstract

For a compact convex subset K of a locally convex Hausdorff space, a measurement on A(K) is a finite family of positive elements in A(K) normalized to the unit constant 1 K, where A(K) denotes the set of continuous real affine functionals on K. It is proved that a compact convex set K is a Choquet simplex if and only if any pair of 2-outcome measurements are compatible, i.e. the measurements are given as the marginals of a single measurement. This generalizes the finite-dimensional result of Plávala (Phys Rev A 94:042108, 2016) obtained in the context of the foundations of quantum theory.

Original languageEnglish
Pages (from-to)1479-1486
Number of pages8
JournalPositivity
Volume24
Issue number5
DOIs
Publication statusPublished - Nov 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Theoretical Computer Science
  • Mathematics(all)

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